Question

Show that the equation of the line that passes through the points (0, b) and (1, b+m) is y=mx+b.

Answer 1

`\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{b})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{b+m}) ~\hfill slope\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{(b+m)}-\stackrel{y1}{b}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{m}{1}\implies m \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{b}=\stackrel{m}{m}(x-\stackrel{x_1}{0}) \\\\\\ y-b=mx\implies y = mx+b`